UC-NRLF 


u 


Harmonic  Exercises 

at  the 

Fianofbrte 

for 

Beginners   and  Advanced  Pupils. 


Forty-two  Exercises 

In 

clear  and  simple   arrangement 


Lu.d.^vrig'  ESix^slei", 


New    York:    G.    Schirmer 

Boston:   Boston  Music   Co. 
Copyright,  1890,  by  the  Publisher, 


Af~rt 


Table  of  Contents. 


Prefmoe  ••••• ••»    VII 

Harmonic  Exercises  at  the  Pianoforte. 

I.  Major  and  Minor  Chords. 

Page  Tf 

§  L    Omajor  Triad ....  1      f  S.  Circle  of  Fifths    •    •    .      S 

First  Exercise.  Fifth  Exercise. 

§  2.    6^-major  Triad .    .    .    •  1      §  6.   Constmction    of    minor 

Second  Exercise.  Triad «      4 

$  a.  F-major  Triad.    .    .    •  fl  Sixth  Exercise. 

Third  Exercise.  |  7.   Major  and  minor  Cliordf 

§  4.   All  the  major  Triads     •  9  in  Circle  of  Fifths    .    •      5 

Fourth  Exercise.  Seventh  Exercise. 

n.   Fisruration. 

I  8.    Figurated  Chords.    •    •      S      §  9.   Subordinate  ExerdiM  •      • 
Eighth  Exercise.  Ninth  Exercise. 

m  Varions  Positions  of  the  Chorda. 

I  to.  Fuidamental  Chord  and 

Inversions  •    •    •    •    •    le 
Tenth  Exercise. 


424838 


IV 


IV.  Fundamental  Triads  of  the  Key. 


I  11.  Dominant  Triad  . 

Eleventh  Exercise. 

I  12.   Subdominant  Triad 

Twelfth  Exercise. 


Page  Page 

•    la      %  IS.   The  Minor  Key  •    •    •    14 

Thirteenth  Exercise. 


13 


Fourteenth  Exercise. 


V.  The  Cadences. 


§  14.  The   Two -chord    and 

Three-chord  Cadences.    15 

Fifteenth  Exercise. 

§  Ifi.  The   Four- chord    Ca- 
dence      17 

Sixteenth  Exercise. 


§  16.   The  Five-chord  Cadence    19 
Seventeenth  Exercise. 

I  17.   Figuration  of  the  Ca- 
dence      •    81 

Eighteenth  Exercise. 

f  18.    Cadences  in  Minor  •    •    S3 
Nineteenth  Exercise. 


VL  The  Dissonaneeg. 


I  19.   Diminished  Triad    •    • 
Twentieth  Exercise. 
Twenty-first  Exercise. 
Twenty-second  Exercise. 

§  20.   Dominant  Chord  of  the 

Seventh 

Twenty-third  Exercise. 

$  21.   Besolution  of  the  Chord 
of  the  Seventh    .    .    . 
Twenty-fourth  Exercise. 


26      f  22.   Positions  of  the  Chord 

of  the  Seventh    ...    80 
Twenty-fifth  Exercise. 
I  23.    Chord   of  the   Seventh 

in  Cadence     .    .    .    .    80 
Twenty-sixth  Exercise. 

28  §  24.    Figuration  of  Chord  of 

the  Seventh    ....    84 
Twenty-seventh  Exercise. 
$  25.    Chords  of  the  Seventh 

29  in  Circle  of  Fourths    .    84 
Twenty-eighth  Exercise. 


Vn.  The  Six  and  Seven-chord  Cadences. 


S  26.    Chord  of  the  Fourth  and 

Sixth 86 

Twenty-ninth  Exercise. 

{  27.   The  Six-chord  Cadence    87 

Thirtieth  Exercise. 

I  28.    In  Minor 89 

Thirty-first  Exercise. 


I  29.    Chord    of  Seventh    on 

Second  Degree    ...    41 
Thirty-second  Exercise. 

§  80.    The  Seven  -  chord   Ca- 
dence      42 

Thirty-third  Exercise. 

§  81.   In  Minor 48 

Thirty-fourth  Exercise. 


Vni.   Chords  in  Diatonic  and  Chromatic  Progression. 


§  32.    Chord  of  the  Sixth .    , 
Thiriy-fifth  Exercise. 
Thirty-sixth  Exercise. 
§  33.    The  Diminished  Triad 
Tiiirty-seventh  Exercise. 


Page 
45 


47 


Pagt 
§  34.    Diminished     Chord    of 

the  Seventh    ....    48 
Thirty-eighth  Exercise. 
§  85.    Chromatic     Chords     of 

the  Sixth 49 

Thirty-ninth  Exercise. 


IX.   Modulation. 


§  36.    Interconnection   .    •    • 

Fortieth  Exercise. 
§  87.   Definition  of  Modulation 
Forty-first  Exercise. 
Forty-second  Exercise. 


51      §  38.   Individuality  of  the  Pu- 
pil, and  proper  limit  of 
69  instruction*    «    •    •    •    66 


Preface. 


The  following  exercises  are  intended  to  sup 
plement  and  further  pianoforte  instruction  by 
teaching  the  elements  of  harmony  through  a 
simple  empirical  method.  Neither  musical  ter- 
minology as  an  essential,  nor  a  systematic  school- 
presentation,  has  been  aimed  at.  The  practical 
performance  of  the  pupil  at  the  instrument  is 
the  sole  object  of  the  course,  which  whenever 
possible  is  to  rely  upon  the  natural  ear,  and  to 
be  assisted,  only  where  this  latter  is  insufficient, 
by  the  merest  external  pedagogic  aids. 

These  exercises  thus  serve  to  develop  the 
musical  sense,  which  experience  proves  to  be 
far  too  easily  slighted  in  piano-teaching. 

Preliminary  studies  are  not  presupposed. 

The  exercises  may  be  interrupted  in  any 
place,  whenever  the  pupU  exhibits  either  dis- 
inclination or  lack  of  comprehension.  Only  a  few 
minutes  in  each  lesson  should  be  devoted  to  them. 


vm 

In  Music-schools  these  exercises  are  suitable 
for  a  half-year  (summer)  piano-course,  which  may 
be  interpolated  between  the  Primary  course  and 
Practical  Harmony,  and  (according  to  the  author's 
experience)  will  afford  the  young  musicians  Uvely 
pleasure. 

Thus  employed  the  Exercises  form  a  pre- 
paratory school,  based  on  simple  empiricism, 
to  a  practical  course  in  Harmony  based  on  a 
; systematic  method, 

Ludwig  Bussler. 


Harmonic  Exercises  at  the  Pianoforte. 


I.   Major  and  Minor  Chords. 

§1. 

C-MAJOR  TRIAD. 
In  the  very  first  piano-lessons  the  C-major  triad 
1. 


m 


should  be  struck  repeatedly.  Derived  from  the  fingering 
of  the  five-finger  exercises  by  keys  touched  with  the  first, 
third  and  fifth  fingers. 

Its  formation  may  be  attempted  simply  by  ear,  after  hearing  it 
struck  several  times.  But  in  the  first  lessons  most  pupils  are  too  em- 
barrassed to  make  such  attempts. 

This  triad  is  called  as  such  the  Chord  of  C-major. 
The  pupil  must  at  all  times  be  able  to  execute  readily  the 
command:  Play  the  chord  of  O-major! 

First  Exercise. 

Chord  of  C-major. 

§2. 
.      G^MAJOR  TRIAD. 

When  the  pupil  can  strike  the  C-major  triad  with  per- 
fect confidence  he  may  form,  at  first  by  ear,  the  6?-major  triad. 

1 


^ 


If  he  cannot  form  it  easily  by  ear,  the  fingering  may 
again  be  called  to  his  aid,  the  position  of  the  keys  being 
precisely  the  same  as  before.  The  chord  so  found  is  to  be 
called  the  Chord  of  6r-major. 

Second  Exercise. 
Chord  of  G-major. 

N.  B.  Where  pupils  do  not  readily  comprehend,  care 
must  be  taken — here  more  than  elsewhere — not  to  push 
forward.  Keep  rather  to  each  exercise— all  of  which  are 
to  be  treated  as  comparatively  unimportant — until  the  pupil 
can  master  it  with  perfect  ease. 

§3. 

^-MAJOR  TRIAD. 
The  ^-major  triad  is  to  be  formed  like  the  above: 
3. 


^ 


in  which,  after  the  ear,  positions  of  the  piano-keys  are  the 
determining  factor. 

Third  Exercise. 

Chord  of  JP-major. 

§  4 

ALL  THE  MAJOR  TRIADS. 

In  the  following  exercise  too  the  ear  must  first  decide, 
i,  ••  the  pupil  should  himself  seek  for  the  tones  forming 
the  Major  triad. 


3 

Pupils  who  quickly  succeed  in  this  easiest  of  harmonic 
exercises,  can  be  taught  the  further  formation  of  chords 
before  gaining  a  knowledge  of  the  notes  and  names  of  the 
black  keys.  Others  should  acquire  this  knowledge  before 
advancing. 

Fourth  Exercise. 

Construct,  first  on  all  white  keys  and  then  on  all 
black  ones,  the  Major  Triads  in  the  order 

4.         F'm&y    C-maj.    G-maj.    2>-maj.    A-m&y    i?-maj.    ^-maj. 


^^ 


W='^'=^ 


^m 


J^tt-maj.      Cft-maj.     ^ib-maj.    J^b-maj.    j?l?-inaj. 


S^^E^J^Ei^ 


^ 


in  case  the  ear  should  not  suffice,  according  to  the  con- 
stant fingering  I,  3,  5. 

The  key-note  (lowest  note)  is  each  time  to  be  named 
or  struck  by  the  teacher. 

This  exercise  is  to  be  continued  until  the  pupil  is  able 
at  any  time,  in  or  out  of  the  order,  to  strike  any  chord 
at  once  and  correctly. 

§5. 

THE  CIRCLE  OF  FIFTHS. 

Let  the  teacher  now  call  for  the  chords  always  in  the 
order  of  the  Circle  of  Fifths: 

0-maj.  G-maj.  D-maj.  -4-maj.  JK-maj.  B-maj.  -Fjt-maj.  Cjt-maj. 

(==  i)t>-maj.) 
Db-maj.  -ib-maj.  ^b-maj.  5b-maj.  J'-maj.  C-maj. 

and  call  the  pupil's  attention  (already  accustomed  to  it  by 
practice)  to  the  interconnection  by  fifths  of  the  key-notes. 


Use  to  this  end  the  mechanical  aid,  that  the  highest  tone 
(fifth  finger)  of  the  foregoing  chord  becomes  the  lowest  tone 
(first  finger)  of  that  following,  finally  allowing  the  pupil  to 
construct  the  succession  of  chords  by  himself. 


a^^^^^i 


Fifth  Exercise. 

Construct  the  Major  Triads  of  the  Circle  of  Fifths. 

Now  show  the  pupil,  that  the  last  chord  is  the  same 
as  the  first. 

The  series  of  chords  therefore  turns  back  to  its  source. 
Thus  it  is  like  a  Circle. 

We  therefore  have  here  a  Circle  of  Chords. 

This  is  called  a  Circle  of  Fifths  because  the  key-notes 
of  the  successive  chords  are  five  tones  (a  Fifth)  apart. 

The  pupil  should  keep  to  this  exercise  until  thorough 
confidence  and  fluency  are  attained. 

The  exercise  should  also  be  played  with  both  hands 
together. 

^ .8^. h 


ns^^i^^^ 


*M^^m 


§6. 

CONSTRUCTION  OF  THE  MINOR  TRIAD. 

The  Minor  Triad  is  formed  from  the  Major  Triad  by 
lowering  the  Third— the  tone  of  the  third  finger. 

(1)  Try  to  construct  minor  chords  by  ear. 

(2)  Construct  the  same  from  major  chords  by  shifting 
third  finder. 


Sixth  Exercise, 
Construct,  from  C-major,   c-minor. 


^=i3*=^t= 


from 

7.     jF-major      /"-minor    ^-major      ^-minor    -(4b-maj<MP      al^-minor 


I 


m=^i=m 


^ 


^i 


-^ 


m 


In  like  maimer  construct  minor  chord  to  every  major 
chord. 

MAJOR  AND  MINOR  CHORDS  IN  THE  CIRCLE  OF  FIFTHS. 

Seyenth  Exercise. 

Major  and  Minor  Chords  in  the  Circle  of  Fifths. 

Let   each  major  chord  in  the  series  of  the  Circle  of 
Fifths  be  followed  by  the  like-named  minor  chord. 

8. 


Later  let  the  left  hand  accompany  these  chords  in  the 
lower  octave.  This  exercise,  closing  a  section,  should  be 
practiced  by  the  pupil  until  he  can  execute  it  almost 
mechanically. 

The  minor  chords  alone  must  also  be  performed 
throughout  the  Circle  of  Fifths. 

Advanced  scholars,  especially  in  class-teaching,  should 
be  made  to  do  all  exercises  in  writing  as  well,  when  this 
does  not  clash  with  the  plan  of  instruction. 


n.  Figuration. 


18. 


A  chord  is  termed  figurated,   when  its   toneg  are  not 
•ounded  together,  hut  separately  in  succession. 

Eighth  Exercise. 

Figurate  the  Major  Chord   ascending  (i.  «•  from 
below  to  above). 


9.      C-major. 


^-major. 


Figurate  the  l^inor  Chord  in  liice  manner: 


¥=t 


10.      C-minor. 


fltf-minor. 


^^ 


^ 


^^m 


tzzt 


Always  hy  heart!    Only  as  shown  hy  the  teacher! 
Left  hand  in  the  lower  octave! 

I^ajor  and  i^linor  Chords  through  the  Circle  of  Fifths 
In  liice  manner: 

u. 


W^^-'^S^^=S^^^^f^rfi^ 


mij;S  'JHJF^^^^ 


l-gf;  t;rjrT\^^=^ 


^^^^^i=fe 


-i«-r^L— jL 


^^ 


^^^ 


S^^^ 


iji^j 


iai^T^  J* 


^^^^^^^^ 


^ 


^ 


g^c^cj:! 


'<>  'j^  i^ 


•to. 


Left  hand  in  the  lower  octave. 

Figurate  the  Chord  ascending  and  descending: 

12. 


In  like  manner  throughout  Circle  of  Fifths. 

Abbreviated  Figuration: 

13.    C-major  ^-minor 


G-major 


^-mmor 


^^^g^^^ 


etc. 


In  like  manner  throughout  the  Circle  of  Fifths. 

The  pupil  should  practice  this  exercise  too  until  per- 
fect confidence  is  gained. 


8 


S9. 

SUBORDINATE  EXERCISES 

which  may  be   omitted   without   disadvantage,  should  the 
course  of  instruction  require  it. 

Ninth  Exercise. 

Figurate  descending  (from  above  to  below)  beginning 
with  the  fifth  finger: 

14.  C-majop 


i=aa-i;j  -ijpfi;- 


As  above  throughout  Circle  of  Fifths. 

15. 


^^^^^^^^^ 


f^^^^^^ 


eta 


Figurate  ascending  and  descending. 


i 


mmf^^ 


etc.  throughout  Circle  of  Fifths. 

This  exercise  will  not  be  as  easy  for  the  pupils  as  it 
may  appear  at  first  glance;  but  like  all  Subordinate  Exer- 
cises, it  is  not  sufficiently  important  to  hold  back  pupils 
who  do  not  readily  comprehend. 

Other  variations  in  figuration  may  here  be  shown  to 
scholars  of  quick  comprehension. 


etc 


^^gg^^^BTi^L'  \3  -^ 


^ 


^^^ 


Siz  etc. 


fe 


•j-io^iij^i-j^iif£[iijij-es=-' 


But  these  already  enter  the  department  of  finger-exer- 
cises to  be  constructed  by  the  pupil  independently,  with 
which  we  have  nothing  to  do. 

Only  a  few  pupils  will  easily  succeed  in  reversing  the 
order  of  the  triads  by  heart,  that  is,  to  play  them  through 
the  Circle  of  Fourths.  The  teacher  must  therefore  usually 
omit  this  exercise.  If  it  be  taken  up  in  rare  cases,  only 
Major  Chords  should  be  employed  at  first. 
18. 


p^^i^^pii^iip 


Here  the  lowest  tone  always  becomes  the  highest  of  the 
chord  next-following,  the  tone  of  the  first  finger  becoming 
the  tone  of  the  fifth  finger. 

The  Minor  chords  follow  in  like  manner: 


19. 


^^^^^s^^i 


10 

With  successive  Msgor  and  Minor  chords  the  Minor 
ehord  comes  first: 


20 


i 


etc. 


But  this  exercise,  as  before  remarked,  is  seldom  so 
easily  to  be  grasped  by  the  pupils  as  should  always  be 
the  case  with  all  exercises  here  given. 


ni.  Various  Positions  of  the  Chords. 

§  10. 
/HE  FUNDAMENTAL  CHORD  AND  ITS  DIVERSIONS. 
Strike  the  Chord  of  0-major 


i 


:.  Now  place  the 


first  finger  on  e,  the  second  on  gr,  and  take  with  the  fifth 
the  upper  c,  omitting  the  lower  c:    ^g 


^ 


We    thus 


obtain  the  second  position  of  the  C-major  chord,  contain- 
ing the  same  tones  in  different  order. 

If  the  teacher  needs  only  to  play,  let  this  suffice. 

Now,  by  beginning  the  succession  of  three  tones  with 
the  third  tone,  gr,  taking  it  with  the  first  finger,  then  c  and 
e  with  the  third  and  fifth  fingers  in  succession,  we  obtain 
the  third  position  of  the  triad: 

21. 


^^1 


The  three  positions  are  therefore; 
22. 


^E 


1=^ 


11 


Tenth  Exercise. 


Construct  the  three  positions  of  the  Triad  through- 
out the  Circle  of  Fifths: 


(I)   in  Major: 


^ 


JOl Ot- 


^ 


'^W 


U 


& 


iSi^Sg^Sf^i^sa 


^st- 


-^?-« 


i=^"^ 


«. 


(2)  in  Major  and  Minor: 

3 aM 


^^=^ 


¥ 


tw 


<5> 1|<9 


If-^ 


:l^^— n rJ 


^^^^^^^%^ 


^ 


2: 


r-^      "    I'g    I'i^ 


12 


i 


(3)  in  Minor: 


^^£=^ 


t^A 

Q.J1J5. 


lEE 


-^^g=Fg-=l= 


i 


2 


22: 


i 


& 


«: 


:Sf=fe=*F=Ei^ 


ii^i 


2^. 


tt- 


^^^^ 


|jS||;^ 


(4)  out  of  regular  order,  when  desired. 

Subordinate.  The  second  Position  is  called  the  iirst 
Iiwersion,  the  third  Position  the  second  Inversion.  The  first 
inversion  is  called  the  Chord  of  the  Sixth;  the  second, 
Chord  of  the  Fourth  and  Sixth. 


IV,  Fundamental  Triads  of  the  Key. 

§.11. 

DOMINANT  TRIAD. 

Three  successive  major  chords  in  the  Circle  of  Fifths 
are  the  Fundamental  Triads  of  the  key  of  the  middle  triad. 


^ 


are    the    fundamental 


For  instance 

triads  of  0-major. 

The  triad  on  the  fifth  degree  is  called,  in  its  relation 
to  the  key,  the  Dominant  triad.  In  the  sign-notation  it  is 
indicated  by  a  Roman  V,  and  sometimes  called  "five"  for 
short 


13 


Eleventh  Exercise. 

Play  Dominant  Triads  of  various  keys,  for  example: 


of  C-major: 


24. 

m 


:,  of  il-major: 


^^1= 


V  V 

Dominant  triads  in  all  positions,  for  example: 


of  C-major: 


r.    25. 

m 


-^ 


i^z=,  of  A\^ 


major: 


72zrtia 


^fezz 


§  12. 

THE  SUBDOMINANT  TRIAD. 

The  ti-iad  on  the  fourth  degree  is  called,  in  its  relation 
to  the  key,  the  Subdominant  Triad. 

In  musical  sign-notation  it  is  indicated  by  a  Roman  IV| 
and  sometimes  called  "four"  for  short. 

Twelfth  Exercise. 

Play  Subdominant  Triads  of  various  keys,  for 
example: 

26 


of  0-major:  |-^y— g — ,  of  il-major:  |A_jg=: 


rv  IV 

The  same  in  all  positions,  for  example: 


27.  ^  ^  ^   ^ 

of  Omajor:  ^(SrT~^~^>  ^^  ^-^major:  \:M!\iI^^^ 


Play  Fundamental  Triads  of  various  Major  Keys: 


of  .4.-major:    TO^     g   "^-^-^ 


IV    I    V 


14 

Likewise  in  the  order  I— IV— V  or  IV— V— I. 
It  will  be  seen,  that  these  three  chords  embrace  all 
seven  tones  of  the  scale. 

BEMARK  (subordinate).  The  fundamental  chords  of  the  Minor  keys 
do  not  stand  next  each  other  in  the  Circle  of  Fifths,  one  of  them 
(the  Dominant  triad  V)  being  a  major  triad.  A  key  formed  of 
three  minor  triads  if  an  impossibility  in  [modem]  musical  logic 

§13. 
THE  MINOR  KEY .• 

Thirteenth  Exercise. 

In  Minor  the  V  (Dominant  triad)  is  a  Major  triad.  We 
know  ("Elements  of  Notation  and  Harmony",  §  40**)  that 
in  the  harmonic  Minor  scale  the  seventh  is  raised.  It  thus 
forms  a  major  third  in  the  dominant  triad. 


Play  Dominant  Triads  of  Minor  Keys,  for  example: 
of  c -minor: 


28. 


ziz,  of  a-minorj 


Fourteenth  Exercise. 

In  Minor  the  IV  (Suhdominant  Triad)  is  a  Minor  chord. 
The  minor  sixth  of  the  harmonic  minor  scale  forms  its  minor 
third. 

Play  Suhdominant  Triads  of  Minor  Keys,  for  example: 


of  c -minor:  -frf  [t    %     ^  of  a -minor: 


•  Advanced  pupils  might  be  told,  that  key  in  the  abstract  sense 
is  called  Mode.    [Translator's  Note.] 

**  By  the  same  author,  also  published  in  English  by  G.  Schirmer, 
New  York.    [Translator's  Note.] 


15 


We  can  now  see,  that  the  chords  were  really  not 
derived  from  the  harmonic  minor  scale,  hut  that  the  latter 
was  formed  from  the  chords.  The  course  of  teaching 
usually  shows  only  the  contrary  (the  key  as  derived  from 
the  scale),  because  the  scales  are  first  learned  and  practiced- 


V.  The  Cadences. 

§  14. 
THE  TWO-CHORD  CADENCE. 
With  the  left  hand  strike  the  fundamental  note  of  flie 
Dominant  triad  in  C-major  S" 


:,  with  the  right  hand 


the  third  position  of  the   same   -frj — g — ;  then  both  to- 
gether: 


^P 


5fc^ 


With  the  left  hand  play  the  fundamental  note  of  tiie 


Tonic    triad   in   C-major 


:,  with  the  right  hand 


the  second  position  of  the  same   -gk    g     ;   then  both  to- 


gether: 


^ 


P 


zz: 


16 


We  have  thus  obtained  a  four-part  Dominant  Triad  and 
a  four-part  Tonic  Triad:  V-— I, 

The  succession  of  these  two  triads  forms  the  simplest 
Cadence,  which  is  called,  because  consisting  of  2  chords,  a 
two-chord  Cadence. 

Fifteenth  Exercise. 
Form  this  Cadence,  (I)  in  C-major: 

32. 


m 


:i=« 


isz 


(2)  In  all  keys  of  the  Circle  of  Fifths: 

83. 


For  learning  to  form  these  and  the  following  Cadences 
many  pupils  need  only  to  hear  them  played.  Some  can  form 
the  cadences  more  easily,  when  they  are  preceded  by  L 

34. 


^ 


^ 


IT. 


-■zf: 


«: 


-JSu 


I     V     I 


17 


To    prevent  misunderstandings   we   give   this   formula 
I— V— I  the  (not  quite  appropriate)  name  of  the 
three-chord  Cadence. 

Form  this  In  all  keys  of  the  Circle  of  Fifths: 

35. 


"7?" 

^ 

— 

-iW 

-«9— 

k 

^~ 

=2Z= 

^ 

-«5»  — 

tfifc 

-?g 

zfcJ 

h -- 

^^ \ 

l-^ 

-6l^ 



-M 

L  ^1 

■ 

I-7J 

-77— \ 

5«?     6>— t 

b|^^-HS=|,J 

5^^=^ 

%A 

^   7 

«9 «5> 

— b<5> 

^ 

^^ ^ 


§  15. 
-      THE  FOUR-CHORD  CADENCE. 
With  the  left  hand  strike  the  fundamental  note  of  the 
Dominant  triad  in  C-^major:   i-?^^~^' 


with  the  right  the 


first  position  of  the  same:    i^— g — ^  Then  strike  both  to- 
gether: 


18 


Set   this    chord   hetween    two  tonic  triads  as  abore 
(No.  31): 

"I 


37. 


<o     fj     <d. 


^ 


i 


^ 


5 


I      IV      I 

This  formula  I— IV— I  is  called  the  Subdominant  or 
Plagal  Close. 

K  we  set  the  Subdominant  chord  in  this  form  between 
I  and  V  of  the  three-chord  cadence,  we  obtain  the  series 

I-IV-V-I 
or  the  four- chord  Cadence. 
38. 


I 


% 


fr- 


:^ 


I     IV    V     I 

Sixteenth  Exercise. 
Form  these,  (I)  in  C-major: 
(2)  in  all  keys  of  the  Circle  of  Fifths: 

Q. — ^—^ — a- 


^m 


^ 


la: 


:g: 


^ 


^^ 


^ 


-^ 


■a-     o. 


5 


zc 


■JSL 


yt r. -H-r4?-^+^^-8«^^M1 r-^: =-41 

¥ 

ffr-'^^-p 

^ 

e, — a. 

1    >v     -"     ^      f,\ 

.  i»   ff^  ■ 

.lA a-1 

\                 \ 

\r-e> *>-n 

19 


,b*  V 


g^ll"^^^^ 


5Hi^ 


^ 


jzazifc 


^1 


^E^^^i^^^^gEpi^izi-:^ 


-^_|Za. 


42^ 


^i=tK 


ztigz: 


T 7^ — ^g=^= 


§  16. 

THE  FIVE-CHORD  CADENCE. 
On   the  sixth  degree  of  every  major  key  there  is  a 


minor  triad 


40. 

m 


22: 


^  r  I  *  »  •  '  » 

This  minor  triad  is  the  tonic  chord  of  the  relative 
minor  key.  [Relative  major  and  minor  keys  are  those 
having  the  same  signature.]  In  the  sign-notation  it  is  in- 
dicated by  a  Roman  VI. 

Seventeenth  Exercise. 

Form  the  triad  on  the  sixth  degree  of  all  major  keys 
In  the  Circle  of  Fifths: 

41. 


I 


^ 


P^t^^fe^^^ 


m- 


\±       rj 


20 


^ 


s 


* 


^ 


^ 


i 


I 


Erect  the  same  triad,  in  all  its  positions,  in  all  keys: 

42.     C-major.  G^-major.      ^  i?-major. 


^ 


^ 


■«- 


(S*- 


^ 


=fif=lg=i«2 


9i 


f^ 


iS: 


^ 


izz: 


etc. 


i^ 


^^^^ 


How  was  the  tonic  triad  formed  in  our  cadences? 

43. 


Answer: 


:g= 


P 


Transpose  Bass  to  the  higher  octare: 


I 


3s: 


i: 


P 


The  above  is  to  be  followed  by  the  triad  on  the  sixth 

degree  in  such  a  way,  that  the  common  tones  c—c"  shall 

be  held  by  the  same  fingers.    To  this  end,  take  with  the 

left  hand  the  fundamental  of  triad  VI  as  near  as  possible 

to  the  fundamental  of  the  foregoing  triad,  i.e.  a  third  lower: 
? — 
.    Now  with  the  right  hand  take  the  third  po- 


1 


•ition  of  triad  VI: 


n 


Then  strike  both  together: 

44. 


i 


ig: 


5t 


Set  this  chord  VI  between  I  and  IV  of  the  foregoing 

cadences.    Thus  we  have  the  five-chord  cadence: 


45. 


^ 


1^ 


^g:= 


9^ 


is: 


I     VI    IV     V      I 

Form  this  cadence  in  all  Iceys  of  the  Circle  of  Fifths: 

46. 


m. 


%- 


|g=r!!S=i^ 


P 


£L  etc. 


P 


122: 


^ 


§  17. 
FIGURATION  OF  THE  CADENCE. 

The  successive  striking  of  the  tones  of  a  chord  is  called 
an  Arpeggio,  broken  Chord,  Figuration.    (§  8.) 

The  playing  in  succession  of  the  tones  of  a  chord  is 
ealled:  to  figurate,  to  play  arpeggios. 


Eighteenth  Exercise. 

Figurate  (I)  the  two-chord  Cadence  in  all  keys: 

Play  the  tones  from  below  upward,  as  eighth-notes. 
47. 


^^^ 


iiEl 


As  a  preparation  the  chords  should  first  be  struck  in 
succession.    (No.  32.) 

C2)  the  three-chord  Cadence  ditto: 

48. 


f^^^^^ 


P 


i 


(3)  the  four-chord  etc 

49. 


^^^^^^^ 


^ 


£ 


--* 


(4)  the  five-chord  etc.: 

60, 


^ff^=f^^^=^=^^m^^ 


-^- 


^m 


23 


§  18. 
TWO  TO  FIVE-CHORD  CADENCE  IN  MINOR. 

This  §  may  be  skipped  entire,  or  kept  until  the  last. 
It  supplements  §  13. 

In  minor  the  V  is  a  major  chord,  the  I  and  IV  minor 
chords. 

The  positions  of  the  chords,  in  both  chords,  are  to  be 
taken  precisely  as  in  major. 


Nineteenth  Exercise, 

Erect  accordingly  (1)  the  V  in  all  minor  keys: 

61. 


1.       c  g  da  e  b  f^ 


^ 


T57 

:30i: 


i^i^* 


V  V         V  V 

^tt  rftt  =  e\? 


^^i^^^^m 


hv 


V 

f 


^^^j-^^^^^^^mi 


P 


(2)  the  IV  in  all  minor  keys: 

52.      0  9  d  "«>„,,/■» 


^-1 


S^ 


S 


^^.^ 


I: 


i^H 


^1 


IV 


24 


gfi       _rf8  =  «l» 


^^^^^^M^=^W=^=li 


^^^^^^^^=^^=m^=^ 


(3)  the  two-chord  Cadence  V  I  in  all  minor  Iceys: 

53. 


^^g^p^^i^p^ 


m 


igr 


-fit. 


22: 


^|i  ^'^ll^ 


^£ 


^^v 


^^ffitefe^ft^ 


a^^g^a^^lp^^ 


jLi,  ^  I        tr  -  r 


U    ->» 


lei^lg^^^^^^l^^ 


3^ "Ig 


fefe 


-«5»- 


la: 


S? 


v^ 


Sl. 


(4)  the  three-chord  cadence  I  V  I: 


^^^^^m 


£d. 


^ 


321 


F[r^ 


3C 


i^ 


etc. 


1 


+ 


25 


(5)  the  plagal  close  I  IV  I: 

56. 


^rg^%^Bg^^^ 


m 


3E 


jo: <^- 


-& <5»- 


-& &- 


7g 77 


M 


g=fc=^ 


*  <g 


^~~g~g^ 


^ 


B 


r.»j 


2z: 


32: 


?■- 


^ 


:^c 


1^ 


11 


SI"P^ 


:2E^ 


i^ 


^£ 


=g=g=^ 


:g=fc=#: 


I 


a« 


3z: 


te 


^ 


p^ 


s 


rpa^ 


3C 


I 


(6)  the  four-chord  cadence  I  IV  V  I: 

56. 


^^Ep; 


;^ 


:a: 


^^^^^=^ 


^wt- 


"^ — Z. — ffi2 — 22" 


1^ 


-«> — <5L 


3?: 


-^—^ 


W^ 


^^Ei^ 


-<5>- 


l^^pl^^^a 


»^ 


-«> <!ii^ 


122: 


26 


(7)  the  five-ohord  oadenoe: 

57. 


(8)  Figurate  the  cadences  in  minor. 

Example  with  the  five-chord  cadence  in  minor: 


=f# 

— rj-#- 

■nr— 

=f1^ 

— ^-1 

-TJ ^^- 

a 

:U= 

-I '  # 

r — 1 

-<9- 

fit. 

"•        ' 

7    J   J* 

1         1 

a 

\f^-^ — 

-1— 

1__ 

r^ 

JJ 

The  close  lacking  in  these  and  other  figurations  can 
he  added  by  a  repeated  (not  figurated)  striking  of  the  last 
ehord. 


VI.  The  Dissonances. 

§  19. 

THE  DIMINISHED  TRIAD. 

On   the  seventh   degree  of  the  key  is  situated  the 
diminished  Triad. — In  C-major: 

59. 


i 


It  will  be  struck,  for  the  purpose  in  hand,  in  all 
keys  with  the  same  fingers  as  the  other  triads,  namely 
1,3,6. 


27 


Twentieth  Exercise. 

Erect  the  diminished  triad  in  all  keys  of  the  Cirote 
of  Fifths: 


The  diminished  triad  is  a  dissonant  chord,  t.  c.  it  must 
be  resolved.  The  resolution  takes  place,  in  the  fingering 
with  the 'two  free  fingers  2  and  4. 


i 


^^fc^ 


Twenty-first  Exercise. 

Form  the  Diminished  Triad,  with  resolution,  in  all 
major  Iceys  of  the  Circle  of  Fifths,  taking  the  same 
fingering  in  all  cases: 


61. 


i^ 


fe 


p^ 


^ 


I^-gEj^i^ 


:^ 


In  minor  keys  the  diminished  ti-iad  is  the  same  as  in 
the  like-named  major  keys,  in  0-minor  as  in  C-major,  in 
il-minor  as  in  ^-major,  etc.  The  fingering  is  consequently 
the  same.  But  in  the  resolution  the  higher  tone  progresses 
a  half-tone  further  down,  the  major  third  of  the  major  key 
being  replaced  by  the  minor  third  of  the  minor  key.  E,  g. 


28 


62.  c-minoT         fl'-minor 


/"D-minor 


P^^^^jig^ 


Twenty-second  Exercise. 

Play  the  diminished  triad,  like  the   others,  in  three 
positions. 

Form  the  three  positions  of  the  diminished  triad  in 
all  keys: 


ii 


W=^ 


22: 


k=^ 


w^w=^ 


■m 


1^^- 


etc. 


20. 


DOMINANT  CHORD  OF  THE  SEVENTH. 

By  adding  above  another  Third  to  the  dominant  triad  V 
we  obtain  a  chord  of  the  seventh,  also  called  Dominant 
Chord  of  the  Seventh. 

64. 


^ 


Twenty-third  Exercise. 

Form  this  chord  of  the  seventh  in  all  keys.  Finger- 
ing: 1,  2,  3,  5.  Here  it  is  better  (musically  more  reasonable) 
to  progress  through  the  Circle  of  Fourths  rather  than  of 
Fifths.  At  first  it  is  easier  to  name  the  key  and  fundamental 
of  each  chord  of  the  seventh. 

Thus:  0-major,  O: 

65. 


F-major,  C; 


m 


29 


Here  too  the  formation  of  the  chords  should  he  assisted, 
as  far  as  possible,  by  the  ear,  especially  when  seeking  the 
fourth  tone  which  completes  the  chord  of  the  seventh.  Below 
are  the 

Chords  of  the  Seventh  in  the  Circle  of  Fourths. 


fe^^ 


=S»J|= 


Figurate  the  chord  of  the  seventh  throughout  the 
Circle  of  Fourths,  upward  and  downwards.  (Compare 
Example  No.  12,  p.  7.) 

§  21. 

RESOLUTION  OF  THE  CHORD  OF  THE  SEVENTH. 

The  three  highest  tones  in  the  chord  of  the  seventh 
form  the  diminished  triad. 

The  right  hand  takes  the  diminished  triad,  and  resolves 
it  as  above: 

67. 


I 


;l^ 


The  left  hand  takes  with  the  thumb  the  fundamental 
of  the  chord,  and  repeats  it  in  the  second  chord  with  the 
addition  of  the  fundamental  of  the  triad,  taken  by  the  little 
finger: 


Together: 


68. 


I 
I 


T 

i 


30 


Twenty-fourth  Exercise. 

Form  accordingly  Dominant  chords  of  the  seventh 
in  all  keys,  with  resolution. 

The  fingering,  which  here  serves  as  a  guide,  must  al- 
ways remain  the  same,  whatever  keys  are  to  be  struck. 

69! 


^mr^i^^^^m^^ 


1=^ 


i=Pi 


22Z32: 


-<S> — <5»- 


I2ZZ5?: 


7J 


j^_x_^_^_ 


H-\^ 


^^^sarjggga^ 


5i3=^i2£* 


^^i^ 


•»•    i9- 


Pt 


>&—& 


% 


l&HIZ. 


^17 


§  22. 
POSITIONS  OF  THE  CHORD  OF  THE  SEVENTH. 

This   chord   having   four   tones,   it   has   likewise   four 
positions: 


figurated: 


Twenty-flfth  Exercise. 

Play  the  Dominant  chord  of  the  seventh  in  all  keys 
and  positions. 


81 


The  first  position  is  called  the  fundamental  chord;  the 
rollowing  are  the  first,  second,  and  third  iuversion*. 
71. 


f: 


I: 


1^ 


S: 


S^ 


t- 


^i 


^^ 


c 


^te 


^i^^ 


^^a^^^^MffSSSp^^Efe^ 


igrns: 


^ 


i3 


-6iL_ ^._. 


=!^ 


^ 


i5i=5 


.€t 


^^ 


^1^^ 


i^^iS^l^fe^^ 


g: 


3:;r5^ 


Play  these  positions  also  with  two  hands,  and  figurate  them. 
§23. 
THE  CHORD  OF  THE  SEVENTH  IN  THE  CADENCE. 

In  the  cadence  the  dominant  seventh  precedes  the  tonie 
triad,  thus  replacing  V.    The  right  takes  the  third  position 

of  the  chord  of  the  seventh: 


g^::,  the  left  hand  the 


fundamental:     9'  ;  together: 

72. 


g^ 


^EE 


32 


Twenty-sixth  Exercise. 

(I)  Erect  dominant  chord  of  the  seventh  in  above 
position  in  all  iceys. 

This  position  is  followed  in  the  cadence  by  the  tonic 
triad,  as  the  latter  before  followed  the  Dominant  Triad  V. 

73. 


ZZL 


g^g: 


(2)  Form  this  two-chord  close  in  all  keys. 

In   all  more   complicated   cadences  the  chord   of  the 
leventh  takes  the  place  of  the  V  (dominant  triad). 

(3)  Form,  with  the  chord  of  the  seventh  instead  of 
the  dominant  triad,  and  in  all  keys 


three-chord  cadences: 

74. 


^ 


:§: 


\k 


S^ffe^ 


-eh—£±- 


f=g^^ 


f  »i^^ 


-^ — g — I 


i 


-«5»- 


U 


etc 


lEE 


la: 


four-chord  cadences 

75. 


^^^^^^^^^^^ 


jQ-. 


-<5> ^ 


[>  O       ^ 


-c^--^ 


I 


^ 


33 


five-chord  cadences: 

76.                                                   „ 
bt 7^- i^ 7^ •;^ /> — \  ff— 

JJ 

1  ^  ^       ^_^_g=:r|_ 

-6»— 

77 

=i-^r^ 

( I. ii_  [JL 





1 «5>-J^ 

tiF=^'^=«=«==-';;==^=^i»? 


'J— g=:gz=; 
-js. 


rg^ 


1^ 


^- 


-0^^ 


■s?-«- 


^ 


.^- 


n——^ 


nA 


ZBT. 


M 


S 


^g^^l^s^^^i^ 


-^L 


*; 


.^- 


fif «fi,TL*. 


■*ifL' 


a 


-g?       ^>    -?; 


^ 


1==?— ^ 


r  ^ 


tjf-^, g « f! TV — cs>- 


^i^l 


-fit. 


is: 


s 


l±i£^ 


-^-^ 


^ 


:S^=:S 


yy ?5^- 


:7=r22z=:a=^ 


±:t?=:g=g=^=gg=g- 


3^^^=^ 


-<5> ^ 


^SQi 


31 


^^i^^^ 


^- 


^ 


s^  « 


^ 


-«> — ^~ 


i 


/ 


§  24. 


FIGURATION  OF  THE  CHORD  OF  THE  SEVENTH. 

In  figurating  the  cadences  the  repetition  of  the  funda- 
mental in  the  chord  of  the  seventh  (right  hand)  is  omitted, 
that  the  rhythm  may  be  equal,  and  we  therefore  play,  not: 


^^m 


Twenty-seventh  Exercise. 

Form  as  above  the  flgurated  five-chord  cadence  in 
all  keys.    Example: 

78. 


I 


^ 


'-f~i-^-^f^-if-C4^ 


^zijrjz^i: 


mi 


p 


£ 


-!(5>- 


§25. 

^      CHORDS  OF  THE  SEVENTH  IN  CIRCLE  OF  FOURTHS. 

Alternate,  while  progressing  through  the  Circle  of 
Fourths,  between  the  first  and  third  positions  of  the  chord 
of  the  seventh  in  the  right  hand: 

Circle  of  Fourths:  C-maj.  ^-maj.  i?l>-inaj.  ^b-maj.  ^b-maj.  i)|?-maj. 
Position:      I.        in  I.  m.  I.  in. 


79. 


1^^^^^^^^ 


Circle  of  Fourths :  i^jj-maj.  ^-maj.  J^-maj.  ^-maj.  i>-maj.  G-m&j.  C-m&y 
Position:        I.  III.         I.         HI.         I.         IH.        I. 

4i 


%=tH 


"ft^ 


Twenty-eighth  Exercise. 

Play  above  series  by  heart  with  the  right  hand. 

The  left  hand  plays  the  fundamental  to  each  chord. 

Play  the  series  with  both  hands: 

80. 


=S^&^ 


^^^^ 


5^ 


■fa. 


-^^     I'"-     ^ 


ia: 


¥^^^r^^=f 


—49- 


The  same  figurated:  (See  No.  70.) 

81. 


$^^^^^^^ 


^ 


^ 


j?r> n- 


(fii- 


p^r^^^^^^^^^^^^^ 


5H|p 


-6*- 


-fS^- 


or: 


36 


Vn.  The  six  and  seven-chord  Cadences. 

§  26. 

CHORD  OF  THE  FOURTH  AND  SIXTH. 

The  second  inversion  (third  position)  of  the  tonie  triad 
is  called  the  Chord  of  the  Fourth  and-  Sixth. 

82. 


m 


Take  this  with  the  right  hand,   douhling  the  lowest 
note  with  the  left: 

83. 


^: 


^EE^ 


giving  chord  of  the  fourth  and  sixth  in  four  parts. 

This  chord  retains  it  significance  as  chord  of  the  fourth 
and  sixth,  when  the  right  hand  takes  another  position  of 
the  triad,  as  long  as  the  hass  is  the  same. 

84. 


I 


-<5»- 


«=^ 


9i 


-ZL 


la: 


Of  these  three  chords  of  the  fourth  and  sixth  we  use 
the  second  in  cadence,  i.  e*  the  one  having  the  tonic  of  the 
key  as  highest  note. 


87 


Twenty-ninth  Exercise. 

Form  the  chord  of  the  fourth  and  sixth  as  above  in 
all  keys. 


85. 


^ 


i& 


P 


W 


^^ 


}<9- 


=^1= 


31=1^ 


i 


^w^. 


^ 


i: 


g 


« 


^ 


9^=^ 


§27. 
THE  SIX-CHORD  CADENCE. 

Play  the  chord  of  the  fourth  and  sixth  given  in  the 
foregoing  §  between  the  third  and  fourth  chords  of  the 
fiye-chord  cadence. 


^^ 


-Kf- 


^ 


^ 


3 


I     VI    IV     I     T 
1     ' 

We  thus  obtain  the  six-chord  cadence. 


Thirtieth  Exercise. 

(I)  Form  the  six-chord  cadence  in  all  major  keys. 

C-migor  as  aboTe.    (No.  86.) 


38 


87.  C-major, 


i>-major. 


13^^^^^ 


«=f 


^ 


^-^-^-^ 


^ 


a 


li 


& — &- 


zzr. 


U- 


^-major. 


^^^i 


etc. 


m^ 


1^: 


•g — a: 


i?t>-inajor. 


^b-major. 


^ 


r:g=g=fn:T^=g; 


5EgE5^?EiE|?Eg 


i^r 


^ 


i^izgzmn 


•6>-      iS>- 


^^^^P' 


Tz: 


-G—&- 


§s?a 


e^ 


^ 


:^-g>    <g- 


^i>-major. 


=g 


-^ — fi^- 


g^ggzzgzzH 


etc. 


.<s, fi ^- 


S 


Figurate 

88.       ^ 

the  six- 

chord  C2 

idence. 

'J  *       ^  J  J       -H"^-^ 

ps — ^ r1 n 

J -^ — H \ 

-^EB 


^ 


g 


f  28. 

m  MINOR. 

Thirty-first  Exercise. 

(I)  Form  in  like  manner  the  tonic  chord  of  the  fourth 
and  sixth  in  all  minor  keys. 

89. 


fei= 


* 


^^ 


W 


=^ 


ZSti 


^ 


^ 


-^^ 


^^- 


!iE 


izs: 


-OL 


m 


^ 


# 


w^^ 


?^ 


teS 


I 


(2)  Form  the  six-chord  cadence  in  minor. 

90.    <;-niinor.  (^-minor. 


ig^g-rgz^^^^ 


^f#g=!^2=^i=r-^g±|^^=|3j^ 


i< 


^ 


-6/         <& 


pa: 


-<5> ^- 


3E 


I     VI  IV     1       f       I 

^-minor. 


<g     fog — ^ 


zc 


eta 


i 


40 


(3)  FIgurated: 

91.    c-minor. 


^^E^i^^^^^ 


m 


ISl 


X r 


JZ. 


m 


^-minor. 


^P 


i^^^i^^^^^ 


^ 


^i=t 


-&- 


3 


BEMAEK.  The  brightest  pupils,  but  only  these,  may  be  told  here, 
that,  instead  of  the  subdominant  triad,  the  chord  of  the  sixth  on  the 
subdominant  (first  inversion  of  the  subordinate  triad  on  the  Second) 
may  be  played. 


Major: 


0^- 

jf~ Ti 7^ ^ 25 -::. V2 

■ 

iy. "      a      » 

\ 

^     ...                        ,               *    , 

_ c 

Figurated 


rrrS^l^^fei^fag^Jrfg 


^ 


s 


-za 


1Z. 


Minor: 


fer^-^^-r-^ 


W- 


ize: 


2E 


41 


I 


Figurated: 


^a. 


tn^zj:; 


^^^^ 


-«?- 


^ 


g 


-<2- 


^ 


2^ 


§29. 

CHORD  OF  THE  SEVENTH  ON  THE  SECOND  DEGREE. 
By  adding  to  the  subdominant  triad  (IV)  a  tUrdi  below, 


g we  obtain  this  chord.    Its  fundamental  is 

the  Second  (second  degree)  of  the  key. 

Thirty-second  Exercise. 

(I)  Form  the  chord  of  the  seventh  on  the  Second 
in  all  major  keys. 

93. 


^ 


^:'-- 


3B2 


^- 


fe 


H- 


=1^ 


i??.- 


ianpi 


^b         E^ 


B)f 


(2)  Form  the  same  chord  so,  that  its  fundamental 
is  taken  an  octave  lower  by  the  left  hand,  the  right 
taking  only  the  subdominant  triad. 


n 


pt 


g= 


5? 


i — <5>. 


S 


£ 


B 


f=f^ 


:es 


#« 


Of 


42 


17<^- 


\ ^rr-  -y^ ,-^g 


^^ 


1 


3±=5i= 


1 


iiii       ^1? 


^b 


§  30. 

THE  SEVEN-CHORD  CADENCE. 

Introduce  the  chord  of  the  seventh  just  explained  be- 
tween the  third  and  fourth  chords  of  the  last  cadence,  i.  «. 
between  the  chords  of  the  subdominant  and  of  the  fourth 
and  sixth. 

95. 


<Z u a Oi ej. <5) Cl 


^ 


^ 


-ISi^II^. 


IV     II7    It 
We  thus  obtain  the  seven-chord  cadence. 


Thirty-third  Exercise. 
(I)  Form  the  seven-chord  cadence  in  all  major  keys. 

96.  u 


gzzg=:g=:gz=:giz^^fiiE=ig=^: 


-.KH    <a        iL|_g. 


s: 


is: 


-G—G- 


43 


(2)  FIgurated. 

97 


|zi:^5Jim1x^^pp^ 


■^ 


.T3t 


^i 


m 


^=1=:^ 


^^^g^^^^^ 


^^t'F^ 


3£& 


::r: 


:3c 


§  31. 
IN  MINOR. 

Thirty-fourth  Exercise. 

(I)  Form  chord  of  the  seventh  on  the  Second,  as 
above,  in  minor.  Only  singly,  because  their  regular  suc- 
cession sounds  disagreeably. 

98. 


^S; 


Jt^ 


^ 


it 


■^i^ 


-^ 


u 


^ 


n     «« 


ipi^^B^i^ 


teszitt: 


g 


44 


(2)  Form  the  seven-chord  cadence  in  minor. 


99.    c-minoT. 


d-mmor. 


-^ 


jO—e^. 


^ 


m 


~cu 


^^^1 L\- 


/9- 


7? 7S 


Si 


^ 


ga^J"     ir— g — ^f    J    -1^^ 


In  forming  these  chords  of  the  seventh  in  minor,  strike  with  the 
right  hand,  as  previously  in  major,  the  subdominant  chord  (IV),  then 
adding  with  the  left  the  lower  third  (Second  of  the  key)  an  octave  below. 

EEMARK.  As  a  subordinate  exercise  the  minor  chord  of 
the  seventh  on  the  seventh  degree  of  the  major  scale 
may  be  taken  up  here.  It  is  resolved  to  the  tonic 
triad,  and  with  this  resolution  exhibits  a  very  clear 
picture  of  the  key,  and  the  mutual  relations  of  its 
seven  tones. 


^Di  A^  g9  B)^  F 


45 

Without  this  resolution  the  chord  does  not  present  the 
major  key  so  clearly,  as  it  may  then  easily  be  mistaken 
for  the  chord  of  the  seventh  on  the  Second  in  minor. 


VIII.  Chords  in  Diatonic  and  Chromatic 
Progression. 

§  32. 
CHORD  OF  THE  SIXTH. 


The  chord  of  the  sixth     ^    g — ;  can  process   dia- 


tonically  in  all  parts,  and  thus  form  a  scale  of  chords  of 
the  sixth  either  ascending  or  descending. 

Thirty-fifth  Exercise. 

Form  scales  of  chords  of  the  sixth,  with  each  hand 
alone,  in  a1  major  Iceys. 

100.  -a.    iSd    ^    za    -a. 


ai 


g-»    s'     "  -^^-^^^-jg-g^ 


u 


^^^^^^^^ 


We  can  proceed  in  like  manner  with  the  chord  of  the 
sixth  and  fourth;  hut  this  series  is  far  less  pleasing  in  effect, 
and  requires  in  composition  a  special  harmonic  actuation. 


46 


Thirty-sixth  Exercise. 

Chords  of  the  fourth  and  sixth  in  diatonic  pro* 
gression. 

101. 


i 


g^^ 


ww^^=^^ 


SElElElEiEE^^ 


■e>—z, 


t^^f^=:«= 


77     ■» 


*     ^      *     S^ 


i^-i^f: 


«: 


=S=g=i=^=S 


^^JEgEJEp^ 


77      -^^ 


'S'— zr 


^ 


^       77 


#=#=1=?=^ 


Ppaa^^^E^P^g^ 


Here  the  best  opportunity  offers  for  a  subordinate  exer- 
cise— that  of  practically  showing  the  pupil  the  nature  of  the 
suspension.  In  C-major  let  him  strike,  hefore  the  highest 
tone  of  each  chord  of  the  sixth,  that  of  the  chord  next 
above,  together  with  the  two  lowest  tones. 

,    I   1  J   I  i  J  J  i 


i 


dz^- 


E 


ii: 


:§ 


^^^^ 


I 


?         ^  ^        i  i       J 


% 


-^ 


^ 


I  I 


•to. 


Variation. 


i 


3     <g     g 


i-.-i-^  ■  ^'  J  -»  ■  '^ 


±=ii 


3z: 


:|!^ 


3= 


<nr  with  tie: 


In  other  keys  the  signature  must  be  carefully  obserred*. 


47 


§  33. 

THE  DIMINISHED  TRIAD. 

The  diminished  triad  may  progress  chromatically,  each 
part  of  the  same  moving  hy  a  semitone  either  ascending  or^ 
descending. 

Thirty-seventh  Exercise. 

102. 


^^^^i^^^Bi^^ 


^^S^^^i^^^ 


This  progression  can  of  course  also  occur  in  Figuration: 


^^ 


1 


^P 


etc. 


i^^p^^^ 


Both  inversions  should  also  he  worked  out: 
First  (chord  of  the  Sixth). 


etc. 


^  J^^^z^ 


c^^-^UB-f^f±§. 


In  Figuration: 


ete. 


9r:^r-^ejJ--t^^^ 


48 


Second  (chord  of  the  fourth  and  sixths 


I 


* 


? 


etc. 


In  Figuration; 


''^  ^  ,  eta 


^iz^j^pd^zt;^^^ 


§  34. 

DIMINISHED  CHORD  OF  THE  SEVENTH. 

For  a  long  period  this  chord  has  occurred  more  fre- 
quently than  any  other  with  the  above  chromatic  pro- 
gression. 

The  diminished  chord  of  the  seventh  consists  of  a 
diminished  triad  with  added  minor  third.  It  therefore  com- 
prises in  all  three  minor  thirds. 

Thirty-eighth  Exercise. 

(I)  Form  the  diminished  chord  of  the  seventh  on 
all  degrees  of  the  chromatic  scale,  with  each  hand  alone. 


103. 


1^^^*!= 


4» 


(2)  Practice  this  succession,  till  thoroughly  fluent, 
In  both  Chords  and  Figuration,  f^rst  with  either  hand 
alone,  then  with  both  together.  (Incidentally,  with  figu- 
ration in  one  hand  and  chords  in  the  other.) 


I 


ife 


m 


eto. 


^^^P 


5*^==^^ 


§  35. 

CHROMATIC  CHORDS  OF  THE  SIXTH. 

These  chords,  and  likewise  those  of  the  fourth  and 
fdxth,  may  progress  chromatically  as  above,  but  with  lesi 
agreeable  effect  than  the  preceding. 

(a)    Chord  of  the  Sixth,  major  triad: 
105. 


^If^Wi-^i^ 


50 


f^^^^ 


et«u 


etai 


eto. 


52 


(b)    C^orc?  o/"  Fourth  and  Sixth  of  same: 
106.         .       .  «_   ^«,_  z^  >#,kfebf  „i;it^  « 


«*g*^^^^ 


^^^^ 


^^^s 


eto. 


eto. 


(o)    Chord  of  the  Siocth,  minor  triadi 

107.  .        . 


^^|^^5p^ 


eta 


(d)    C%or({  0/*  JFVmrfA  am2  <Sfia?fA,  minor  ^rtod; 

108. 


51 


^^^^ 


ete. 


Thirty-ninth  Exercise. 
Form  such  progressions. 


IX.  Modulation. 

§36. 

INTERCONNECTION. 

Those  chords  which  stand  next  each  other  in  the  Circle 
of  Fifths  or  Fourths  are  termed  interconnected  (related). 

Major  and  minor  chords,  whose  keys  have  like  signatures, 
are  called  relative. 

Fortieth  Exercise. 

(I)  Play  major  triads,  with  their  relative  minor  triads, 
throughout  the  Circle  of  Fourths. 

c       F       B\f       e:\^       A\^        J)>  i^S 


^&^g^p^p3i^pto^ 


•         i  g  t  f  V}  d% 

B  E  A  V—^       e  C 


^m 


Major  and  minor  chords  having  the  same  fundamental 
are  called  like-named.  The  exercise,  to  play  the  like-named 
triads,  haa  already  been  given.    (Seventh  Exercise.) 

4* 


52 


^  (2)  Pass  from  a  major  triad  to  the  like-named  minor 

triad,  from  this  to  its  relative  major  triad,  which  is  then 
to  he  treated  similarly. 


'^^. 


^S^S^igp^tj^ 


w^ 


\w%W^^- 


^%- 


a-pjyg^' 


a 


^ 


equal  to 


$^^^^^^^^"^^i^^P 


Application: 


etc. 


like-named    \  interconnected  \ 

relative 


N^^#^^ 


f77      >^ 

2 


etc. 


§  37. 


DEFINITION  OF  MODULATION. 

The  transition  (passing  over)  to  another  key  is  called 
Modulation. 

The  series  of  chords  of  the  seventh  in  Nos.  79—81 
modulates  with  each  progression;  t.  e.  each  chord  of  the 
series  helongs  to  a  different  key.  ' 

Rules  for  modulation  can  he  presented  only  in  a  sys- 
tematic and  methodic  course  of  Harmony.  Here  all  must 
be  left,  after  a  mere  passing  suggestion,  to  the  talent  and 
inclination  of  the  pupil.  More  serious  endeavors  should  be 
based  on  the  exercise  of  practical  harmony* 


ftS 


A  Modulation  is  effected  by  the  introduction  and  reg- 
ular resolution  of  the  dominant  chord  of  the  seventh  be- 
longing to  that  key,  into  which  we  wish  to  pass. 

111. 

From  C-major  to  6?-inajor. 


=f-|^l^ 


^: 


-O 


i.  «.  by  the  two-chord  caden<}e  6f  tne  new  key.  The  two- 
chord  cadence  forms,  as  we  know,  the  two  last  chords 
(and  the  most  essential  part)  of  all  cadences. 

Also,  the  three  last  chords  of  the  seven-chord  cadence 
may  be  used  for  modulation;  of  course  we  always  mean  the 
cadence  of  that  key,  into  which  we  wish  to  pasa. 

112. 
From  C'-major  to  6?-major. 


w 


w 


Also,  the  four  last  chbri 
113 


xbrds: 


?   ^ 


i 


t=t 


■^—^-. 


'W^^'^^ 


^ 


-G- 


Also,  the  five  last  chords 


L    V 


i 


7    X    • 
114.    From  ^-minor  to  C-major. 


f-f-i-g-^^ 


^. 


IV     1 


>'\r^  V-]   i 


64 


Also,  the  six  last  chords: 

115.    From  ^-major  to  (7-major. 


L ^—G <^ 


g=g=g^g=: 


«: 


^i 


<9- 


la: 


«9- 


Forty-flrst  Exercise. 

Modulate  by  the  two-chord  cadence  from  any  key 
into  any  other. 

Here  no  heed  should  be  given  to  the  progression  and 
leading  of  the  individual  parts,  unless  the  pupil's  talent 
fairly  demands  it. 

Should  the  chord  of  the  seventh  in  the  new  key  not 
follow  harmoniously  upon  the  first  chord,  a  related  triad 
may  he  introduced  between  the  two. 

116. 


^^J^I^PHig^i^ 


95 


-12^ 


iza: 


Instead  of  a  triad  we  may  introduce  a  dominant  or 
diminished  chord  of  the  seventh,  or  one  on  the  second  de- 
gree, whereby  the  pupil  however,  from  his  present  stand- 
point, can  not  be  guided  by  rules,  but  exclusively  by  his 
ear  and  taste. 


117. 


-t2^ 


^ 


Xi. 


55 


Forty-second  Exercise. 

Modulate  with  the  two-chord  cadence  and  a  chord 
previously  introduced. 

§  38. 

UPON  THE  INDIVIDUALITY 

of  tlie  pupil  it  will  depend  whether,  or  at  what  stage,  the 
teacher  shall  begin  with  the  systematic  exercise  of  prac- 
tical harmony.  Upon  this  only  it  also  depends,  how  far 
the  teacher  shall  let  him  work  out  the  exercises  here  pre- 
sented, and  whether  any  or  many  may  be  skipped  or  no. 
More  especially  the  exercises  in  minor  are  often  repugnant 
to  less  gifted  or  zealous  pupils,  in  which  case  they  may 
be  left  out.  On  the  other  hand,  the  teacher  may  pay  more 
attention  to  the  minor  keys  than  has  been  done  above, 
whenever  a  pupil  exhibits  the  necessary  intelligence  and 
interest.  For  instance,  the  resolution  of  the  diminished  triad 
and  dominant  chord  of  the  seventh  may  also  be  carried 
out  in  minor;  the  key  of  the  diminished  chord  of  the  seventh 
may  be  determined,  the  chord  followed  through  its  in- 
versions, and  resolved  to  major  and  minor.  Peculiarly  tal- 
ented pupils  may  also  attempt  to  follow  up  and  vary  the 
cadences  through  inversions. 

Still,  with  such  gifted  pupils,  it  is  always  better  to 
proceed  to  systematic  instruction. 

We  must  again  repeat,  that  the  foregoing  exercises 
have  no  further  purpose  than  to  awaken  and  increase  in- 
terest in  the  harmonic  foundation  of  modern  music;  that 
they  hereby  purposely  avoid  systematic  completeness,  ap- 
pealing only  to  the  musical  power  of  perception,  to  the  ear, 
and  aiding  the  latter,  wherever  necessary,  by  helps  of  a 
quite  external  nature.    They  thus  form,  in  a  degree,  an 

harmonic  Kindergarten, 
a  preliminary  course,  based  simply  on  empiricism,    to  the 


56  '^e. .<:..;...    -.,:;.«,. ^; 

jsystematic  method  of  harmony,  but  quite  self-dependent, 
and  independent  of  the  latter,  forming  a  supplement  to  the 
practical  course  of  music,  which  is  especially  useful  in 
piano-teaching.  With  most  other  instruments,  the  player's 
own  production  of  the  tones  is  beneficial  to  the  musical 
perception.  Yet  they  too,  although  perhaps  in  a  less  de- 
gree, require  this  supplementary  course,  an  application  of 
which  to  other  instruments,  or  in  singing-lessoniSi,  offers  no 
difficulty. 


-ogSo- 


/  , 

/ 

■     ..      .         /-                            /w. 

'^- 

j 

:^ 

0  -   --^/ 

/ 

.^"""^^ 

1 

-z-   f  —y'  Y  ~f.  o 

7  :  tt7 


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